I think there is a difference between allegations and judgements. Judgements are ultimately a public record in the United States.

Stuff like credit records are different, but even then I think transparency goes a long way. Asking Google to forget your unpaid rent has some meaning, but it also doesn't meaningfully address the issue -- private entities will privately keep track of check and credit issues.

IMO, once you do something, the genie is out of the bottle in terms of the hit to your reputation. Obscuring it isn't necessarily helpful. Perhaps the real solution is figuring out how to stop applying harsh moral judgements for mistakes. If you bounced a check or were involved in a crime in 2001, and we're in 2018 and you don't have a pattern of misbehavior, someone should either not consider that long ago action or have to positively explain why that event was a factor in a decision process.